Stability and inertia theorems for generalized Lyapunov equations

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Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations (2009, methodology): “…strangeness index, Lyapunov exponent, Bohl exponent, Sacker-Sell spectrum, exponential dichotomy, spectral interval, smooth QR factorization, continuous QR algorithm, discrete QR algorithm, kinematic equivalence, Steklov function AMS(MOS) subject classification: 65L07, 65L80, 34D08, 34D09”
Analysis and Numerical Solution of Generalized Lyapunov Equations (2002, background): “arise in many fields of mathematics and engineering such as stability analysis for differential and difference equations [53, 61, 123, 148, 149], problems of spectral dichotomy [62, 113, 116] and control theory [11, 58, 98, 117, 119, 176].”
Stability analysis of positive descriptor systems (2008, methodology): “For descriptor systems, generalised projected Lyapunov equations were presented in [39].”
Krylov subspace methods for projected Lyapunov equations (2012, background): “We assume that the pencil λE − A is stable, i.e., all its finite eigenvalues have negative real part.”